The description of the eigenfunctions of the Beltrami-Laplace operator on the arbitrary homogeneous pseudo-Riemannian symmetric space of rank 1. In general the Beltrami–Laplace operator is ultrahyperbolic one in this case. The integral Fourier–Mellin–Whittaker transform transforming the Beltrami–Laplace operator in the horosperical coordinates to the ordinary differential operator was constructed. The inversion formula was received. The number of papers (with M. A. Olshanetsky) were devoted to the integral representations of the modified $q$-Bessel functions and $q$-Macdonald functions. The $q$-Fourier transform and the inversion formula were constructed in the space of the distributions. The $q$-convolution and its $q$-Fourier transform are defined. The unitary irreducible representations of the quantum Lorentz group are constructed and their connection with the quantum relativistic Toda chain is determined.
Main publications:
Rogov V.-B. K. $q^2$-Convolution and its $q^2$-Fourier transform // Czechoslovk Journal of Physics, 2000, 50(11), 1347–1352.
